The Science of Patterns

Mathematics can be thought of as the science of patterns; when we study math we are always looking to see if there is an underlying pattern that can be used to create an equation; finding the equation is one of the basic tasks of mathematics; today we will start with looking for patterns within maps of the United States. I say maps because we will be looking at different data sets and how they are represented with a map. Click on the link labelled maps and use the tool to answer the following questions:

1. Which state has the most land area and how much area does it have?

2. Which state has the most people per square mile?

3. If you wanted to move to a state with the most open land, which one would you choose?

4. Where is the most gas used per person? Why do you think this is?

Tell Me a Story; Give Me an Account.

Another way of asking someone to tell you a story is to say: "Would you please give me an account of what you have been doing. An account is a story; Likewise when you put money in the bank they place it in an account; if we look at the account over time it can tell us a story about what has happened to our money. There are many tools on the Internet for helping you see what happens to money over time. Today we will use one of those tools. Click on the link on the right called "The Money Tool " and answer the questions below on the comment link.

1. If you put $100 to start your account and you add $100 per month, how much will you have after five years.


2. Interest is the amount of money the bank will give you for letting them use your money; how much interest did the bank pay you over five years on the plan in number 1?


3. Let's say you bought your first car with a credit card; the car cost $3000; if it takes you five years to pay off that credit card how much did you end up paying for the car?



4. If you open a stock market account with $100 and add $100 per month; how much money will you have after five years?

A Grain of Rice

There is an old story about a grain of rice that is a famous math problem. In a kingdom long ago a poor man saved the son of the king from drowning; the king told the man he would give him 1000 gold coins as a reward; the poor man said all he wants is one grain of rice on the first day of the month and double the amount each day of the month. The king was surprised; he told the man he was a good man for asking for so little.



Here is the math problem. Here is the question: if the man has one grain of rice on the first day; two on the second day and four on the third day; how many grains of rice will he have after 30 days?



Use the calculator and google to solve the problem.



Step 2: Click on the link to the right called A Grain of Rice. For every question you get right rice is donated to the poor by The United Nations. Find the math problems on the site and see if you can make it to level 10.

Mathematical Thinking

Finding patterns is one of the foundations of mathematical thinking; Often we need tools to help us find a complex pattern; games can be used as a tool to find patterns and express them in algebraic terms; the game called NIM is one of those tools. Your challenge today is to learn how to play Nim against the computer. Nim is a take away game similar to the one we played in class; in this case your opponent can take away only as many buttons as you take; the object of the game is to pick the last remaining buttons. Click on the link to the right to begin the game. Once you are able to bear the computer with 20 buttons call a teacher over and show them your skill.

Problem Solving and Technology

Technology is a tool that can be helpful as part of a problem solving strategy. Models that were made by hand in the past are now made on computers with virtual machines called applets. Today we are going to use technology to help us solve a problem: what are the best gears to use on a bicycle when I want to get to a friends house as fast as possible. The link on the right is an applet that will help us answer the question. Read the instruction, play the game and then answer the questions below.

1. If my friends house is in the city two miles away on flat ground, which two gears would get me there as fast as possible?

2. Why would I ever want to use the two slowest gears?

3. If you could only choose one pair of gears which would you choose and why?

4. How many possible choices would you have on the bike used in the applet?